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What I Tell You Three Times Is True

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Raymond Smullyan on Self Reference

Part of the book series: Outstanding Contributions to Logic ((OCTR,volume 14))

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Abstract

A very brief look at self reference in literature and art.

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Notes

  1. 1.

    Sterne (2003), pp. 5–6, 8.

  2. 2.

    i.e., This is not a pipe.

  3. 3.

    i.e., Attempt of the impossible.

  4. 4.

    Thanks to Judith Dunford who called my attention to this example.

  5. 5.

    Gödel (1995), p. 307. in his address Gödel suggested that analytic number theory already goes beyond first order number theory. But in later work, Feferman and Takeuti, have independently shown that much of classical analysis can be formalized in a conservative extension of Peano Arithmetic. I am not aware of any investigations of how this applies to analytic number theory.

  6. 6.

    For some of his early examples see Friedman (1998). His web site https://u.osu.edu/friedman.8/ has many more examples.

References

  • Friedman, H. (1998). Finite functions and the necessary use of large cardinals. Annals of Mathematics, 148, 803893.

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  • Gödel, H. (1995). Some basic theorems on the foundations of mathematics and their implication. In S. Feferman, et al. (Ed.), Collected works, (vol. III, pp. 304–323). Oxford.

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  • Mancosu, P. (1996). Philosophy of mathematics & mathematical practice in the seventeenth century. Oxford.

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  • Smullyan, R. (1986). This book needs no title: A budget of living paradoxes. Paperback: Touchstone Books.

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  • Smullyan, R. (1994). Diagonalization and self-reference. Oxford.

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  • Sterne, L. (2003). The life and opinions of Tristram Shandy, gentleman, First published 1759–67. Penguin paperback edition.

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Author information

Authors and Affiliations

  1. New York University and University of California, Berkeley, USA

    Martin Davis

Authors
  1. Martin Davis
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Correspondence to Martin Davis .

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Editors and Affiliations

  1. City University of New York (CUNY) System, City University of New York, New York City, New York, USA

    Melvin Fitting

  2. NYC Department of Education, Brooklyn, New York, USA

    Brian Rayman

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Davis, M. (2017). What I Tell You Three Times Is True. In: Fitting, M., Rayman, B. (eds) Raymond Smullyan on Self Reference. Outstanding Contributions to Logic, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-68732-2_8

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